1. Field of the Invention
The present invention relates generally to the field of frequency domain signal processing. More specifically, the present invention discloses a filtering apparatus to prevent signal aliasing in frequency domain measurements of the type performed by digital oscilloscopes and spectrum analyzers.
2. Statement of the Problem
Many oscilloscope users have a need to view signals in both the time domain (input voltage as a function of time) and the frequency domain (input voltage as a function of frequency). This need has been partially met by the use of the fast Fourier transform ("FFT") on time domain data in a conventional digital oscilloscope. However, this method can result in signal aliasing--where the digitized signal bears no real relationship to the actual input signal. Aliasing occurs when the sample rate of the digital oscilloscope is relatively near the input frequency. For example, consider a situation with a sample rate of 10 KHz and an input signal in the form of a sine wave whose frequency differs from the sampling frequency by 0.1%. (e.g. 10 KHz+10 Hz, or 10,010 Hz). Aliasing will cause the digitized signal to appear as a sine wave having a frequency of 10 Hz, not 10.01 KHz.
Aliasing is prevented if the input signal is sampled at a rate greater than twice the highest frequency present in the input signal. This is known as the Nyquist limit. Therefore, one solution to aliasing is to add circuitry (e.g. a low-pass filter) to bandwidth limit the input signal below the Nyquist limit before it is digitized. A number of approaches have used in the past to address the problem of aliasing:
Digital Oscilloscope with Fixed Filter. FIG. 4 shows a simplified block diagram of a conventional digital oscilloscope operating in FFT mode with a single analog low-pass filter 10. The filter has a fixed cut-off frequency which bandlimits the input signal to prevent aliasing at the highest sample rate. The input signal is then sampled and digitized by an analog-to-digital convertor 20 ("ADC") controlled by a variable clock 30. The digitized data is stored in a memory 40 for subsequent processing by the FFT processor 50 which generates a frequency domain display. However, it is important to note that the sample rate of the ADC 20 can be adjustably reduced below the maximum sample rate as a function of the timebase setting for the oscilloscope display (i.e. time / div.) selected by the user. Since the cut-off frequency of the low-pass remains fixed even if the sample rate is reduced, the oscilloscope is not alias-protected to the extent the sample rate is reduced below the Nyquist limit for the input signal. In other words, the anti-aliasing filter 10 is completely effective only at the highest sample rate.
Digital Oscilloscope with Selectable Filters.
The situation can be improved to a degree by adding a bank of selectable analog low-pass filters as shown in FIG. 5. In general, a separate low-pass filter is required for each sample rate (i.e. for each timebase setting) of the oscilloscope. Since oscilloscopes commonly have many timebase settings, this approach requires twenty or more individual filters. For example, a 100 MHz oscilloscope typically has 26 distinct timebase settings ranging from 5 sec/div to 2 nsec/div. Therefore, the disadvantage of this approach is the large number of filters required.
FFT Spectrum Analyzer.
FFT spectrum analyzers use a different system architecture to implement a frequency domain measurement based on the FFT, as shown in FIG. 6. An analog low-pass filter 10 bandlimits the input signal. The ADC 20 samples at a fixed rate, f.sub.s, which is high enough relative to the cut-off frequency of the filter 10 to prevent aliasing. Bandwidth reduction is achieved by means of a digital filter 35 such as a finite impulse response ("FIR") filter. After the bandwidth has been reduced, the sample rate can also be reduced without losing information by means of a decimator 38 which discards all but every k.sup.th sample. The analog low-pass filter 10 can be viewed as providing alias protection for the digital FIR filter 35, while the digital FIR filter 35 provides alias protection at the reduced bandwidth and sample rate output by the decimator 38. Unfortunately, since the ADC 20 operates at a fixed sample rate, f.sub.s, the digital FIR filter 35 must also process the data in real time at this same rate. The sample rate is effectively limited by the speed of the digital filter hardware, and at high sample rates (e.g. greater than 25 MHz) the hardware requirements of this approach become very difficult to implement.
Digital Oscilloscooe with Post-Acquisition Digital Filter. FIG. 7 provides a block diagram of an approach which alleviates the problem of having to operate the digital filter 35 in real time at the full sample rate. In this approach, a memory 25 is placed in front of the digital filter 35. The sampled data from the ADC 20 is stored in the memory and the digital filter 35 can operate on the data at less than real time. In order not to miss any samples, the memory must be large enough to hold all of the unfiltered sample data required by the digital filter 35. This dictates a very large memory. For example, 10 seconds of data at a sample rate of 400 MHz would require a memory size of 4 gigasamples. Alternatively, if the memory is limited to a reasonable size, the range of sample rates is limited, which in turn limits the range in input frequencies that can be accurately represented.
In addition to previously discussed approaches, a number of existing patents disclose solutions to the problem of signal aliasing, including the following:
______________________________________ Inventor Patent No. Issue Date ______________________________________ Hansen, et al. 4,802,098 Jan. 31, 1989 Saxe, et al. 4,621,217 Nov. 4, 1986 ______________________________________
Hansen, et al., disclose a digital bandpass oscilloscope in which the input signal is first filtered by an analog low-pass filter 12, converted to digital form by a digitizer 16, processed by a waveform data processing unit 18 which quadrature modulates, decimates and low-pass filters the digital data to provide waveform data sequences a(m) and b(m) which are stored in memory 20. FFT analysis is provided by a microprocessor 22 acting on the data sequences stored in the memory 20. The architecture of this portion of the Hansen system is similar to a conventional FFT spectrum analyzer, as discussed above and shown in FIG. 6. The disadvantage of this approach is that the waveform data processing unit 18 must process the data in real time at the sample rate of the digitizer 16. As previously mentioned, this is difficult to implement at high sample rates.
Saxe, et al. disclose an anti-aliasing filter arrangement for oscilloscopes that is a variation on the conventional approach of using a selectable bank of analog filters shown in FIG. 5. A plurality of selectable analog low-pass filters 17, 18, and 19 are used at the higher sweep rates. However, a "digital transversal filter" 32 is used at the lowest band. This filter is actually an analog implementation of a finite impulse response filter, requiring analog delay, multiplier, and sample and hold circuitry. This arrangement is effectively a variation on the idea of using a bank of selectable low-pass filters, as shown in FIG. 5.